18,083 research outputs found
Totally balanced combinatorial optimization games
Combinatorial optimization games deal with cooperative games for which the value of every subset of players is obtained by solving a combinatorial optimization problem on the resources collectively owned by this subset. A solution of the game is in the core if no subset of players is able to gain advantage by breaking away from this collective decision of all players. The game is totally balanced if and only if the core is non-empty for every induced subgame of it. We study the total balancedness of several combinatorial optimization games in this paper. For a class of the partition game [5], we have a complete characterization for the total balancedness. For the packing and covering games [3], we completely clarify the relationship between the related primal/dual linear programs for the corresponding games to be totally balanced. Our work opens up the question of fully characterizing the combinatorial structures of totally balanced packing and covering games, for which we present some interesting examples: the totally balanced matching, vertex cover, and minimum coloring games.link_to_subscribed_fulltex
LP-games and combinatorial optimization games
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Production-inventory games and PMAS-games: characterizations of the Owen point
Production-inventory games were introduced in [Guardiola, L.A., Meca, A., Puerto, J. (2008). Production-Inventory games: A new class of totally balanced combinatorial optimization games. Games Econom. Behav. doi:10.1016/j.geb.2007.02.003] as a new class of totally balanced combinatorial optimization games. From among all core-allocations, the Owen point was proposed as a specifically appealing solution. In this paper we study some relationships of the class of production-inventory games and other classes of new and known games. In addition, we propose three axiomatic characterizations of the Owen point. We use eight axioms for these characterizations, among those, inessentiality and additivity of players’ demands are used for the first time in this paper
"Combinatorial Bootstrap Inference IN in Prtially Identified Incomplete Structural Models"
We propose a computationally feasible inference method infinite games of complete information. Galichon and Henry (2011) and Beresteanu, Molchanov, and Molinari (2011) show that such models are equivalent to a collection of moment inequalities that increases exponentially with the number of discrete outcomes. We propose an equivalent characterization based on classical combinatorial optimization methods that alleviates this computational burden and allows the construction of confidence regions with an effcient combinatorial bootstrap procedure that runs in linear computing time. The method can also be applied to the empirical analysis of cooperative and noncooperative games, instrumental variable models of discrete choice and revealed preference analysis. We propose an application to the determinants of long term elderly care choices.
On the Concavity of Delivery Games
Delivery games, introduced by Hamers, Borm, van de Leensel and Tijs (1994), are combinatorial optimization games that arise from delivery problems closely related to the Chinese postman problem (CPP). They showed that delivery games are not necessarily balanced. For delivery problems corresponding to the class of bridge-connected Euler graphs they showed that the related games are balanced. This paper focuses on the concavity property for delivery games. A delivery game arising from a delivery model corresponding to a bridge-connected Euler graph needs not to be concave. The main result will be that for delivery problems corresponding to the class of bridge-connected cyclic graphs, which is a subclass of the class of bridge-connected Euler graphs, the related delivery games are concave.
Solving generic nonarchimedean semidefinite programs using stochastic game algorithms
A general issue in computational optimization is to develop combinatorial
algorithms for semidefinite programming. We address this issue when the base
field is nonarchimedean. We provide a solution for a class of semidefinite
feasibility problems given by generic matrices. Our approach is based on
tropical geometry. It relies on tropical spectrahedra, which are defined as the
images by the valuation of nonarchimedean spectrahedra. We establish a
correspondence between generic tropical spectrahedra and zero-sum stochastic
games with perfect information. The latter have been well studied in
algorithmic game theory. This allows us to solve nonarchimedean semidefinite
feasibility problems using algorithms for stochastic games. These algorithms
are of a combinatorial nature and work for large instances.Comment: v1: 25 pages, 4 figures; v2: 27 pages, 4 figures, minor revisions +
benchmarks added; v3: 30 pages, 6 figures, generalization to non-Metzler sign
patterns + some results have been replaced by references to the companion
work arXiv:1610.0674
Frank-Wolfe Algorithms for Saddle Point Problems
We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained
smooth convex-concave saddle point (SP) problems. Remarkably, the method only
requires access to linear minimization oracles. Leveraging recent advances in
FW optimization, we provide the first proof of convergence of a FW-type saddle
point solver over polytopes, thereby partially answering a 30 year-old
conjecture. We also survey other convergence results and highlight gaps in the
theoretical underpinnings of FW-style algorithms. Motivating applications
without known efficient alternatives are explored through structured prediction
with combinatorial penalties as well as games over matching polytopes involving
an exponential number of constraints.Comment: Appears in: Proceedings of the 20th International Conference on
Artificial Intelligence and Statistics (AISTATS 2017). 39 page
Optimal Algorithms for 2 x nAB Games--A Graph-Partition Approach
[[abstract]]This paper presents new and systematic methodologies to analyze deductive games and obtain optimal algorithms for 2 ? n AB games, where n ? 2. We have invented a graphic model to represent the game-guessing process. With this novel approach, we find some symmetric and recursive structures in the process. This not only reduces the size of the search space, but also helps us to derive the optimum strategies more efficiently. By using this technique, we develop optimal strategies for 2 ? n AB games in the expected and worst cases, and are able to derive the following new results: (1) ?n/2? + 1 guesses
are necessary and sufficient for 2 ? n AB games in the worst case, (2) the minimum number of guesses required for 2 ? n AB games in the expected case is (4n3 + 21n2 - 76n + 72)/12n(n - 1) if n is even, and (4n3 + 21n2 - 82n + 105)/12n(n - 1) if n is odd.
The optimization of this problem bears resemblance with other computational problems, such as circuit testing, differential cryptanalysis, on-line models with equivalent queries, and additive search problems. Any conclusion of this kind of deductive game may be applied, although probably not directly, to any of these problems, as well as to any other combinatorial optimization problem.
Matroids are Immune to Braess Paradox
The famous Braess paradox describes the following phenomenon: It might happen
that the improvement of resources, like building a new street within a
congested network, may in fact lead to larger costs for the players in an
equilibrium. In this paper we consider general nonatomic congestion games and
give a characterization of the maximal combinatorial property of strategy
spaces for which Braess paradox does not occur. In a nutshell, bases of
matroids are exactly this maximal structure. We prove our characterization by
two novel sensitivity results for convex separable optimization problems over
polymatroid base polyhedra which may be of independent interest.Comment: 21 page
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